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We must build a crate with square top and bottom whose volume is 8000 cubic inches....

We must build a crate with square top and bottom whose volume is 8000 cubic inches. The material for the top and the bottom costs $0.09 per square inch; the material for the sides costs $0.05 per square inch. What (exact) dimensions minimize the total cost? What is the total cost (to the nearest cent)?

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